Finite-Time Set Reachability of Probabilistic Boolean Multiplex Control Networks

Yuxin Cui,Yunxiao Shan,Shu Li,Fengqiu Liu

doi:10.3390/app12020883

Abstract

This study focuses on the finite-time set reachability of probabilistic Boolean multiplex control networks (PBMCNs). Firstly, based on the state transfer graph (STG) reconstruction technique, the PBMCNs are extended to random logic dynamical systems. Then, a necessary and sufficient condition for the finite-time set reachability of PBMCNs is obtained. Finally, the obtained results are effectively illustrated by an example.

Highlights

The Boolean network (BN) is a discrete dynamic model proposed by Kauffman [1,2] in 1969 to represent complicated gene regulatory networks in an accessible and effective manner
Compared with detailed kinetic models of biomolecules, BNs may be useful in understanding the dynamic key properties of regulatory processes when they are applied to biological systems [3,4,5], computer systems [6,7], and power systems [8], and other fields
The feedback stabilization problem of probabilistic Boolean control networks (PBCNs) was studied based on the model-free reinforcement learning technique in [29]

Summary

Introduction

The Boolean network (BN) is a discrete dynamic model proposed by Kauffman [1,2] in 1969 to represent complicated gene regulatory networks in an accessible and effective manner. The STP of matrices is an expansion of ordinary matrix multiplication, which breaks through the limitation of ordinary matrix multiplication on dimension Based on this method, many achievements [10,11,12,13] related to BNs have been obtained. Switched Boolean control networks (SBCNs) are further proposed by adding deterministic switching signals to the BCNs, and it is suitable for modeling biological systems. In [27], the finite-time controllability and set controllability of impulsive PBCNs were investigated On this basis, a model-free reinforcement learning technique [28] was proposed to solve the control problem in gene regulatory networks.

Problem Setting

Finite-Time Set Reachability

State Transfer Graph

Result and Discussion

Conclusions